Lucas Number Calculator

Use our free Lucas number calculator to generate the Lucas sequence (L₀=2, L₁=1), test numbers, or compute Lₙ for a given n.

Math

Mode

How Many

Number

Position (n)

Formula

Lucas numbers follow the Fibonacci recurrence Lₙ = Lₙ₋₁ + Lₙ₋₂ but with different starting values: L₀ = 2, L₁ = 1. The sequence is 2, 1, 3, 4, 7, 11, 18, 29, 47, ...

L₀ = 2, L₁ = 1, Lₙ = Lₙ₋₁ + Lₙ₋₂

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode: generate, check, or position.
2Click Calculate to see the result.

Examples

First 5 Lucas

1.L₀=2, L₁=1, L₂=3, L₃=4, L₄=7

Result: 7

Check 47

1.47 = L₈, 47 is a Lucas number

Result: Yes

L₁₀

1.L₁₀ = 123

Result: 123

Frequently Asked Questions

A sequence with the Fibonacci recurrence but L₀=2, L₁=1.

Lₙ = Fₙ₋₁ + Fₙ₊₁. Also Lₙ = φⁿ + ψⁿ (Binet-form).

Lₙ/Lₙ₋₁ also approaches φ ≈ 1.618.

L₀ = 2, unique to Lucas numbers.

Lucas numbers can be used in the Lucas–Lehmer test for Mersenne primes.

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CalculateMe Team

Last updated: 2026-07-14

Lucas Number Calculator

Formula

How It Works

Examples

First 5 Lucas

Check 47

L₁₀

Frequently Asked Questions

What are Lucas numbers?

Relation to Fibonacci?

Golden ratio?

L₀?

Primality?

Related Calculators

Lucas Number Calculator

Formula

How It Works

Examples

First 5 Lucas

Check 47

L₁₀

Frequently Asked Questions

What are Lucas numbers?

Relation to Fibonacci?

Golden ratio?

L₀?

Primality?

Related Calculators